# Difference between convolution and correlation

What is the difference between these two operations in signal processing except that convolution= folding + correlation? Can we say Convolution is a measure of similarity between two signals?

What is the difference between these two operations in signal processing except that convolution= folding + correlation? Can we say Convolution is a measure of similarity between two signals?

## Popular Answers

Raymond Phan· Ryerson UniversityCorrelation is measuring how similar two signals are to each other, and convolution is directly related to the impulse response, or the output of a system would be, given that you provide a unit impulse into the system. Once you know the impulse response, convolution can essentially determine what the output of your system is, due to any arbitrary input that you provide to it.

## All Answers (22)

Cataldo Guaragnella· Politecnico di BariConvolution, instead, is the common operation a Linear and Time Invariant system can perform on a given input signal.

It is clear that, in specific cases, correlation anc convolution are very similar: the matched filter case makes correlation and convolution identical.

Deepak Kumar Rout· National Institute of Technology RourkelaRamesh Babu.N· VIT UniversityConvolution is the product of two signals in frequency domain.

Mathematically you can say convolution = folding + Corr.

Hossein Soleimani· Isfahan University of TechnologyAbdelaziz A. Abdelhamid· University of AucklandRaymond Phan· Ryerson UniversityCorrelation is measuring how similar two signals are to each other, and convolution is directly related to the impulse response, or the output of a system would be, given that you provide a unit impulse into the system. Once you know the impulse response, convolution can essentially determine what the output of your system is, due to any arbitrary input that you provide to it.

Manuel Duarte Ortigueira· New University of LisbonDinesh Ramegowda· AmazonConvolution -> linear operation on the signal / signal modifier

Farid Kadri· Université Kasdi Merbah OuarglaYou can use correlation to compare the similarity of two sets of data. Correlation computes a measure of similarity of two input signals as they are shifted by one another. The correlation result reaches a maximum at the time when the two signals match best

convolution is used to compute the output of a certain linear system when a certain input signal is applied to it. this is done by applying convolution between the input signal and the impulse response of the system

Ulrich G. Hofmann· Universitätsklinikum FreiburgMike Sousa·"Correlation = measure of similarity between two signals

Convolution -> linear operation on the signal / signal modifier"

In words:

convolution used to determine the output of some linear system. This is done by performing convolution between an input response of the linear system and the input signal being applied to that linear system

correlation will show the similarities of two signals, as correlation is performed on the two signals, it will maximize at the time where their similarities are greatest.

Olivier Laligant· University of BurgundyDo not forget to take into account the energy of the signals: to obtain a useful measure of similarity between two signals, normalize (divide) the correlation by the square root of the product of the autocorrelation (max) of each signal.

Example:

Assume you want to know the correlation between cos(pi.t/2) and (1-t^2) on the range [-1;1] for t. You obtain the correlation function (32/pi^3).cos(pi.T/2) where T is the shift parameter. It follows the max (T=0) is 1.03 !!! Verifying the correlation between cos(pi.t/2) and itself, you will obtain 1. Does it mean (1-t^2) is more correlated to cos(pi.t/2) than cos(pi.t/2) itself ? Obviously, no!

If you normalize the correlation operation, the normalized correlation function between cos(pi.t/2) and (1-t^2) is as follows: ((32/pi^3)/(16/15x1)^1/2).cos(pi.T/2). The max is then 0.9992 (less than 1, ok).

Rk: 16/15 is the max of the autocorrelation of (1-t^2) and 1 is the max of the autocorrelation of cos(pi.t/2), all on the range [-1;1].

Mahmood Hameed· University of KansasCorrelation is obtained by shifting one of the signals over the complex conjugate of the other while multiplying and adding common elements (for continuous: it is integration of overlapping area).

Olivier Laligant· University of BurgundyCorrelation is a mathematical tool and does not model linear system even convolution can be written as a correlation.

Practically, the impulse response can be observed thanks to an impulse signal at the input. Unfortunately, it is not accurate enough (lacking of energy to excite the system) and we use the correlation (!) between a noisy input signal and the output to obtain the impulse response.

Samuel James· Karunya University--Auto-correlation where similarities of signal with itself in variation of time.

(e.g) detection of periodicity of noise in annual sunspot.

--Other hand cross-correlation is finding similarities between two different signals..

Convolution:

which can be used to find the response a system/act as a filter..

Just choosing of "impulse response" you can find the response of the system.

--If you want to play musical keyboard with different instruments like drums, take impulse response of drums(h(t)) and keyboard note which you are playing is x(t), so when you convolute the both you will get the keyboard*drums (effect of drums will change according to the keyboard note which you played).

Mehdi Julayusefi· University of TehranTeodor Petrita· Polytechnic University of Timisoarahttp://www.youtube.com/watch?v=Ma0YONjMZLI

check the matlab link also

.

The convolution is meeting of two signals, the OLDEST part of one signal with the OLDEST part of the other signal, while in the correlation one signal "catches" the other one from behind, by sliding.

So you can consider correlation a measure of coincidence of two signals, while convolution a result of a composition of two signals.

A line wave equation is A=A0 cos (j omega t - k r).

Why minus? Why not +? Time and distance are ascending, why they are not both +?

Because from the generator first is coming out the OLDEST part of the signal, so the signs of ascendant signal (in time) and ascendant signal (in distance) are different.

Hope it helps.

Archana Pawar· VNR Vignana Jyothi Institute of Engineering & TechnologyFernando Soares Schlindwein· University of LeicesterSeth Stewart· Brigham Young University - Provo Main CampusCorrelationis an exact similarity measure between two functions K (the kernel, filter, or template) and S (the signal under test). It answers the questions, "(1)Wherein the signal S are these two functions most similar, and (2)How similarare they at that point?" The similarity measure is computed at pointtas the dot product of a copy of the kernel function translated bytwith the signal under test.Convolution is identical to correlation except that the kernel is flipped before correlation.

Convolution is only a measure of similarity between two signals if the kernel is symmetric, making the problem equivalent to correlation.

Convolution is useful because the flipping of a kernel in its definition makes convolution with a delta function equivalent to the identity function. When using a transform such as the Fourier transform to reconstruct a signal as a linear combination of some set of basis functions, this identity property is indispensable because the spatial continuity of the output signal with respect to the input signal is preserved (the system is causal), whereas correlation would output values in reverse order.Can you help by adding an answer?